The boys, aged nine and ten, got into difficulty on a building site near the Jack Kane Centre.
A man in a nearby flat managed to rescue one of the boys but became stuck in the mud himself while trying to release the other youngster.
A spokeswoman for Lothian and Borders Fire and Rescue Service said: “One child had been with the boys but did not get stuck in the mud and went home to tell his mum, who called the fire service.
“A male adult in nearby flats heard the children calling out and went to their aid. He managed to release one of the boys but got stuck releasing the second.”
Firefighters were called to the scene just after 7pm yesterday, with crews from Newcraighall, Marionville, Tollcross and Liberton attending, using a nine-metre ladder to rescue them.
The adult refused treatment, while the children were taken to the Edinburgh Sick Kids hospital as a precaution.
* A STRETCH of the city bypass was brought to a standstill after a car caught fire.
The incident, which took place on the eastbound carriageway between Dreghorn and Lothianburn at around 6pm last night, led to the closure of two lanes as fire crews tackled the blaze.
It is not believed anyone was injured. Lothian and Borders Fire and Rescue Service received 25 calls reporting the incident as traffic queued up in rush hour.
* ONE of the Capital’s leading restaurants has closed its doors, less than a year after an extensive refurbishment.
The Vintners Rooms, in Leith, has been forced to shut after its owner admitted customer levels had dwindled, despite undergoing a £40,000 revamp which saw the addition of a whisky lounge.
The closure of the restaurant comes after several other high-profile eateries went down the same path.
Oner Giuseppe Begnoni said: “The Vintners Rooms was losing too much money. We had a lot of tourists coming into the whisky lounge, but not enough local people. The restaurant just wasn’t busy enough.
“I’d consider leasing it out again but, at the moment, the plan is to sell the site off.”
* THE One Show’s Matt Baker is to attempt to cycle a rickshaw from Edinburgh to London in eight days to raise money for BBC Children in Need.
The TV presenter will embark on his arduous 484-mile journey on the morning of November 11 from Edinburgh Castle Esplanade.